Dependence of the relaxation rate of coherent states on the number of correlated spins and the order of coherence

The relaxation of the components of the multiple-quantum NMR spectrum of a solid under the effect of the dipole–dipole interactions during the evolution period is considered. It is taken into account that clusters of dynamically correlated spins of different sizes are formed in the preparatory period, and their degradation depends on their size and coherence order. To calculate the size distribution function of clusters and their degradation function, a physical model including relaxation processes is developed. Using this model, an analytical result for a multiple-quantum spectrum is obtained. Agreement is obtained between the theoretical and experimental dependences of the coherence degradation rates in adamantane scaled by the square root of the average cluster size. The parameters of the above functions are found from the comparison of these dependences.